Question: A circle has a circumference of ${8}$. It has an arc of length $\dfrac{32}{5}$. What is the central angle of the arc, in degrees?
The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$. $\dfrac{{\theta}}{360^\circ} = \dfrac{{s}}{{c}}$ $\dfrac{{\theta}}{360^\circ} = {\dfrac{32}{5}} \div {8}$ $\dfrac{{\theta}}{360^\circ} = \dfrac{4}{5}$ ${\theta} = \dfrac{4}{5} \times 360^\circ$ ${\theta} = 288^\circ$ ${8}$ ${\dfrac{32}{5}}$ ${288^\circ}$